Solve for $z$, $ -\dfrac{z + 4}{8z - 20} = \dfrac{10}{2z - 5} + \dfrac{4}{2z - 5} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8z - 20$ $2z - 5$ and $2z - 5$ The common denominator is $8z - 20$ The denominator of the first term is already $8z - 20$ , so we don't need to change it. To get $8z - 20$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{10}{2z - 5} \times \dfrac{4}{4} = \dfrac{40}{8z - 20} $ To get $8z - 20$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{4}{2z - 5} \times \dfrac{4}{4} = \dfrac{16}{8z - 20} $ This give us: $ -\dfrac{z + 4}{8z - 20} = \dfrac{40}{8z - 20} + \dfrac{16}{8z - 20} $ If we multiply both sides of the equation by $8z - 20$ , we get: $ -z - 4 = 40 + 16$ $ -z - 4 = 56$ $ -z = 60 $ $ z = -60$